Quantum Uncertainty Structures

Quantum Uncertainty Structures - A Bayesian Approach to Quantum Randomness, is the first full-sized monograph on the implications of Bayesian probability theory in regards to the structural elements and procedures of quantum information. The irreducibility and algebraic features of quantum randomness are introduced through a discussion of Bell-type inequalities and the Kochen-Specker theorem in terms of the interplay of quantum states, PVMs, POVMs, and Kraus rule. The, the meaning of the analysis of randomness is considered in terms of probability theory from stated first principles, concluding that it refers to the coherent and adaptive arrangement of personal uncertainty. Finally, the elements comprising the structural framework of quantum information, namely, quantum states and operations, are shown to be uncertainty encoding structures much in the same way as probability assignments, albeit with intriguing differences explored throughout the book. Algebraic structures such asentangled quantum states and SIC-POVMs, which are well known in the applications of quantum information processing, are proven to be instrumental in this setting, thus strengthening their relevance.
Significant features of the book include:
first and comprehensive monograph on a Bayesian approach to quantum information
clear and thorough discussion of foundations and implications
detailed description of algebraic procedures and analytical results
a novel analysis of Kraus rule as a conditioning procedure
further emphasis on the significance of SIC-POVMs in regards to quantum information
This book will be of interest to a wide audience, ranging from graduate-level students in physics, mathematics and philosophy, to senior researchers in the fields of quantum theory and quantum information, linear algebra, operator theory on Hilbert space, probability theory, philosophy, or the history of physics.
The book is self-contained, with only a basic working knowledge of the elements of